Preheat oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground turkey to the skillet and cook, breaking it apart with a spoon, until no longer pink, about 6-8 minutes.
Stir in diced red bell pepper, zucchini, and sliced mushrooms. Cook for 5 minutes until vegetables are tender.
Add drained diced tomatoes, dried Italian seasoning, salt, and black pepper. Stir to combine and cook for 2 minutes.
Remove skillet from heat and stir in cooked brown rice and half of the shredded mozzarella cheese.
Transfer the mixture to a 9×13 inch baking dish and spread evenly.
Sprinkle the remaining mozzarella cheese and grated Parmesan cheese evenly over the top.
Cover the baking dish with aluminum foil and refrigerate if making ahead, or bake immediately.
To bake immediately: Bake covered for 25 minutes, then remove foil and bake an additional 15 minutes until cheese is melted and bubbly.
If baking from refrigerated: Bake covered for 35 minutes, then remove foil and bake an additional 15 minutes until heated through and cheese is melted.
Remove from oven and let stand for 5 minutes before serving.